From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is :

• h²/4R

• 3h/4

• 5h/8

• 3h²/8R

From a solid sphere of mass M and radius R, a cube of the maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is

3.

A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension

• angular momentum is conserved

• angular momentum changes in magnitude but not in the direction

• angular momentum changes in direction but not in magnitude

• angular momentum changes in direction but not in magnitude

A metallic rod of length ‘l’ is tied to a string of length 2l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the e.m.f. induced across the ends of the rod is

This question has Statement I and Statement II. Of the four choices given after the Statements, choose the
one that best describes the two Statements.
Statement – I: A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as f 
Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

• Statement – I is true, Statement – II is true, Statement – II is a correct explanation of Statement – I.

• Statement – I is true, Statement – II is true, Statement – II is not a correct explanation of Statement – I.

• Statement – I is true, Statement – II is false.

• Statement – I is true, Statement – II is false.

A hoop of radius r and mass m rotating with an angular velocity ω₀
is placed on a rough horizontal surface.The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

• rω₀/4

• rω₀/3

• rω₀/2

• rω₀/2

A diatomic molecule is made of two masses m₁ and m₂ which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by (n is an integer)

A cylindrical tube, open at both ends, has a fundamental frequency, f, in the air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now

• m₁r₁:m₂r₂

• m₁ :m₂

• r₁ :r₂

• r₁ :r₂

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc 

• remains unchanged

• continuously decreases

• continuously increases 

• continuously increases 

Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d < < l) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate.As a result the charges approach each other with a velocity v. Then as a function of distance x between them

• v ∝ x^-1

• v ∝ x^1/2

• v ∝ x

• v ∝ x